# Investment Calculations

Sheet1

Problem 18-1A convertible bond has a \$1,000 face value and a conversion ratio of 45. What is the conversion price?(Round your answer to 2 decimal places. Omit the “\$” sign in your response.)A convertible bond has a \$1,000 face value and a conversion ratio of 31. What is the conversion price?(Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Conversion price\$   Explanation:\$1,000 / 45 = \$22.2232.2580645161Sheet2

Problem 18.2 (6e)A convertible bond has a conversion ratio of 22 and a par value of \$1,000. What is the conversion price?(Round your answer to 2 decimal places. Omit the “\$” sign in your response)A convertible bond has a conversion ratio of 36 and a par value of \$1,000. What is the conversion price?(Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Conversion price\$   Explanation:\$1,000/22 = \$45.4527.7777777778Sheet3

Problem 18-2A company just sold a convertible bond at a par value of \$1,000. If the conversion price is \$58, what is the conversion ratio? (Round your answer to 2 decimal places.)  Conversion ratio   Explanation:\$1,000 / \$58 = 17.2423.2558139535Sheet4

Problem 18-3A convertible bond has a \$1,000 face value and a conversion ratio of 36. If the stock price is \$42, what is the conversion value? (Omit the “\$” sign in your response.)A convertible bond has a \$1,000 face value and a conversion ratio of 42. If the stock price is \$39, what is the conversion value? (Omit the “\$” sign in your response.)  Conversion value\$  Explanation:36 × \$42 = \$1,5121638Sheet5

Problem 18.5 (6e)A convertible bond has a conversion ratio of 17 and a par value of \$1,000. If the stock is currently priced at \$38, what is the conversion value? (Omit the “\$” sign in your response.)A convertible bond has a conversion ratio of 34 and a par value of \$1,000. If the stock is currently priced at \$22, what is the conversion value? (Omit the “\$” sign in your response.)  Conversion value\$   Explanation:17 × \$38 = \$646748Sheet6

Problem 18.6 (6e)Consider a convertible bond with a conversion value of \$1,120. The stock is currently priced at \$33. What is the conversion ratio of the bond? (Round your answer to 2 decimal places.)Consider a convertible bond with a conversion value of \$1,200. The stock is currently priced at \$38. What is the conversion ratio of the bond? (Round your answer to 2 decimal places.)  Conversion ratio    Conversion ratio  Explanation:31.5789473684\$1,120/\$33 = 33.94Sheet7

Problem 18-4A bond matures in 25 years, but is callable in 11 years at 123. The call premium decreases by 2 percent of par per year. If the bond is called in 16 years, what percent of face value will you receive? (Omit the “%” sign in your response.)  Bond call price in 16 years %  Sheet8

Problem 18-5You own a bond with a 7.4 percent coupon rate and a yield to call of 8.3 percent. The bond currently sells for \$1,095. If the bond is callable in five years, what is the call premium of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Call premium\$   Sheet9

Problem 18-20Steven Long, a bond analyst, is analyzing a convertible bond. The characteristics of the bond are given below. Convertible Bond Characteristics  Par value\$1,000  Annual coupon rate (annual pay)6.3%  Conversion ratio29  Market price118% of par  Straight value99% of parUnderlying Stock Characteristics  Current market price\$31 per shareCompute the bond’s conversion value and conversion price. (Round your conversion price to 2 decimal places. Omit the “\$” sign in your response.)  Conversion value\$     Conversion price\$   Sheet10

Problem 18-20Steven Long, a bond analyst, is analyzing a convertible bond. The characteristics of the bond are given below.Convertible Bond Characteristics  Par value\$1,000    Annual coupon rate (annual pay)7.2%    Conversion ratio25  Market price105% of par    Straight value99% of par  Underlying Stock Characteristics  Current market price\$32 per share  Compute the bond’s conversion value and conversion price. (Omit the “\$” sign in your response.)  Conversion value\$     Conversion price\$   Sheet11

What is the price of a STRIPS with a maturity of 3 years, a face value of \$10,000, and a yield to maturity of 7.2 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Price of a STRIPS\$   Yield to maturity % Sheet12

A STRIPS with 14 years until maturity and a face value of \$10,000 is trading for \$7,000. What is the yield to maturity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Yield to maturity %Sheet13

Problem 18-11A municipal bond with a coupon rate of 3.9 percent has a yield to maturity of 4.9 percent. Assume a face value of \$5,000. If the bond has 5 years to maturity, what is the price of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Price of the bond\$   Sheet14

Problem 18-12A municipal bond with a coupon rate of 5.60 percent sells for \$4,890 and has eight years until maturity. What is the yield to maturity of the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Yield to maturity of the bond %  Sheet15

Problem 19.6 (6e)A municipal bond has 10 years until maturity and sells for \$5,661. If the coupon rate on the bond is 6.83 percent, what is the yield to maturity? (Round your answer to 2 decimal places. Omit the “%” sign in your response.)  Yield to maturity %  Sheet16

Problem 18-13A municipal bond has 18 years until maturity and sells for \$5,190. It has a coupon rate of 3.90 percent and it can be called in 8 years. What is the yield to call if the call price is 105 percent of par? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Yield to call %  Sheet17

Problem 19.8 (6e)A municipal bond has a yield to maturity of 4.8 percent. What corporate bond yield would make an investor in the 34 percent tax bracket indifferent between the two bonds, all else the same? (Round your answer to 2 decimal places. Omit the “%” sign in your response.)A municipal bond has a yield to maturity of 4.8 percent. What corporate bond yield would make an investor in the 34 percent tax bracket indifferent between the two bonds, all else the same? (Round your answer to 2 decimal places. Omit the “%” sign in your response.)  Bond yield %  Explanation:3.80%/(1 – .29) = 5.35%7.27%Sheet18

roblem 18-14A taxable corporate issue yields 6.5 percent. For an investor in a 35 percent tax bracket, what is the equivalent aftertax yield? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)A taxable corporate issue yields 6.8 percent. For an investor in a 35 percent tax bracket, what is the equivalent aftertax yield? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Aftertax yield %  Explanation:6.50%(1 – .35) = 4.23%6.80.654.42Sheet19

Problem 18-15A taxable issue yields 6.4 percent, and a similar municipal issue yields 4.7 percent. What is the critical marginal tax rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)A taxable issue yields 6 percent, and a similar municipal issue yields 4.5 percent. What is the critical marginal tax rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Tax rate%  Explanation:1 – .047 / .064 = 26.56%0.25Sheet20

Problem 18-16A Treasury bill has a bid yield of 3.5% and an ask yield of 3.44%. The bill matures in 155 days. Assume a face value of \$1,000. What is the least you could pay to acquire a bill? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the “\$” sign in your response.)  Price\$   Sheet21

Problem 18-17A Treasury bill has a bid yield of 2.01% and an ask yield of 1.97%. The bill matures in 158 days. Assume a face value of \$1,000. What is the dollar spread for this bill? (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the “\$” sign in your response.)   Dollar spread\$   Sheet22

Problem 18-18A Treasury issue is quoted at 128:16 bid and 128:30 ask. Assume a face value of \$1,000. What is the least you could pay to acquire a bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Price\$   Sheet23

Problem 19.14 (6e)A noncallable Treasury bond has a quoted yield of 5.13 percent. It has a 6.1 percent coupon and 12 years to maturity.a.What is its dollar price assuming a \$1,000 par value? (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Dollar price\$   b.What is its quoted price?  Quoted price :   Sheet24

Problem 18-19A Treasury bond with the longest maturity (30 years) has an ask price quoted at 98:02. The coupon rate is 3.60 percent, paid semiannually. What is the yield to maturity of this bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Yield to maturity %  Sheet25

Problem 18-24A STRIPS traded on May 1 2014, matures in 10 years on May 1 2024. Assuming a 6 percent yield to maturity, what is the STRIPS price? (Use Excel to answer this question. Enter your answer as a percentage of par value. Round your answer to 4 decimal places. Omit the “%” sign in your response.)  STRIPS price\$   Sheet26

Problem 18-25A STRIPS traded on May 1 2014, matures in 10 years on May 1 2024. The quoted STRIPS price is 84.35. What is its yield to maturity? (Use Excel to answer this question. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)  Yield to maturity %  Sheet27

Problem 20-3A homeowner takes out a \$397,000, 30-year fixed-rate mortgage at a rate of 5.30 percent. What are the monthly mortgage payments? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Mortgage payment\$   Sheet28

Problem 20-4You have decided to buy a house. You can get a mortgage rate of 5.85 percent, and you want your payments to be \$1,000 or less. How much can you borrow on a 15-year fixed-rate mortgage? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Mortgage amount\$  Sheet29

Problem 20-8A 30-year, \$240,000 mortgage has a rate of 5.3 percent.1What are the interest and principal portions in the first payment? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “\$” sign in your response.)  Interest\$     Principal\$   2What are the interest and principal portions in the second payment? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “\$” sign in your response.)  Interest\$     Principal\$   Sheet30

Problem 20-9A homeowner takes a 20-year fixed-rate mortgage for \$180,000 at 7 percent. After five years, the homeowner sells the house and pays off the remaining principal. How much is the principal payment? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)    Principal payment\$   Sheet31

Problem 20-10Consider a 15-year, \$120,000 mortgage with a 5.85 percent interest rate. After four years, the borrower (the mortgage issuer) pays it off. How much will the lender receive? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)    Lender receives\$   Sheet32

Problem 20-11Consider a 30-year, \$140,000 mortgage with a rate of .0620 percent. Thirteen years into the mortgage, rates have fallen to 5 percent. What would be the monthly saving to a homeowner from refinancing the outstanding mortgage balance at the lower rate for the same maturity date? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “\$” sign in your response.)  Savings\$   22.22 ± 1%

22.22 ± 1%

45.45 ± 1%

45.45 ± 1%

17.24 ± 1%

17.24 ± 1%

1,512 ± .1%

1,512 ± .1%

646 ± 1%

646 ± 1%

33.94 ± 1%

33.94 ± 1%

6.49 ± 1%

6.49 ± 1%

4.64 ± 1%

4.64 ± 1%

4.86 ± 1%

4.86 ± 1%

5.35 ± 1%

5.35 ± 1%

4.23 ± 1%

4.23 ± 1%

26.56 ± 1%

26.56 ± 1%

.084 ± 1%

.084 ± 1%

108

108

1,084.40

1,084.40

14

14

4.63 ± 1%

4.63 ± 1%

5.40 ± 1%

5.40 ± 1%

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